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In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of:: is same as that on the right side of::? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) X:56::84:Y
X = 96, Y = 54
X = 92, Y = 48
X = 108, Y = 62
X = 98, Y = 32
X = 92, Y = 48
Observe that 84 is 1.5 ├Ч56(56тИЧ1.5=84).Check the options for a pair (X, Y) where Y is exactly 1.5 times X (or X = Y / 1.5).
Observe that 84 is 1.5 ├Ч56(56тИЧ1.5=84).Check the options for a pair (X, Y) where Y is exactly 1.5 times X (or X = Y / 1.5).
Analyze the given relationship
The relationship is X: 56:: 84: Y. Comparing the known numbers 56 and 84, we see that 84 / 56 = 1.5. Therefore, the ratio between the first and second number in both pairs is 1.5 (Second = First * 1.5 or First = Second / 1.5).
Test the options using the 1.5 ratio
We need X = 56 / 1.5 (which is not an integer) or rather the pattern 56 / X = Y / 84. Rearranging the proportion: X / 56 = 84 / Y. So, X * Y = 56 * 84 = 4704.
Verify Option B
Testing Option B (X = 92, Y = 48): 92 * 48 = 4416 (Incorrect). Testing Option A (X = 96, Y = 54): 96 * 54 = 5184 (Incorrect). Testing the logic again: Looking at the relationship 56 and 84, 56 * 1.5 = 84. Checking the options again, for X = 92 and Y = 48: 92 * (84/56) = 92 * 1.5 = 138 (No). Checking X = 92, Y = 48 relation: 92 - 44 = 48. 56 - 44 = 12 (No). Checking X = 92, Y = 48: 92 / 2 = 46 + 2 = 48. 56 / 2 = 28 + 2 = 30 (No). Re-evaluating: The ratio 84/56 = 3/2. Thus, X/Y = 56/84 = 2/3. For X = 92, Y = 48: 92/48 = 23/12 (No). For X = 92, Y = 48: 92 is 56+36, 84 is 48+36. Yes, 92 - 56 = 36 and 84 - 48 = 36. The difference between the numbers in each pair is constant: 84 - X = Y - 56 is not it. It is 92 - 56 = 36 and 84 - 48 = 36. The difference is consistent.
A: 96-56=40 and 84-54=30 (No); C: 108-56=52 and 84-62=22 (No); D: 98-56=42 and 84-32=52 (No). Only B provides a consistent additive difference of 36 between the corresponding terms (92-56=36 and 84-48=36).
B is correct because the difference between the first and second number in both pairs is constant: 92 - 56 = 36 and 84 - 48 = 36.
When ratios fail in number analogies, always test the difference between corresponding terms to see if a constant value is added or subtracted across both pairs.
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